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For low-dimensional metallic structures, such as nanotubes, the exchange coupling between localized magnetic dopants is predicted to decay slowly with separation. The long-range character of this interaction plays a significant role in determining the magnetic order of the system. It has previously been shown that the interaction range depends on the conformation of the magnetic dopants in both graphene and nanotubes. Here we examine the RKKY interaction in carbon nanotubes in the presence of uniaxial strain for a range of different impurity configurations. We show that strain is capable of amplifying or attenuating the RKKY interaction, significantly increasing certain interaction ranges, and acting as a switch: effectively turning on or off the interaction. We argue that uniaxial strain can be employed to significantly manipulate magnetic interactions in carbon nanotubes, allowing an interplay between mechanical and magnetic properties in future spintronic devices. We also examine the dimensional relationship between graphene and nanotubes with regards to the decay rate of the RKKY interaction., Comment: 7 pages, 6 figures, submitted

The indirect exchange interaction is one of the key factors in determining the overall alignment of magnetic impurities embedded in metallic host materials. In this work we examine the range of this interaction in magnetically-doped graphene systems in the presence of armchair edges using a combination of analytical and numerical Green function (GF) approaches. We consider both a semi-infinite sheet of graphene with a single armchair edge, and also quasi-one-dimensional armchair edged graphene nanoribbons (GNRs). While we find signals of the bulk decay rate in semi-infinite graphene and signals of the expected one-dimensional decay rate in GNRs, we also find an unusually rapid decay for certain instances in both, which manifests itself whenever the impurities are located at sites which are a multiple of three atoms from the edge. This decay behavior emerges from both the analytic and numerical calculations, and the result for semi-infinite graphene can be interpreted as an intermediate case between ribbon and bulk systems.

The growing interest in carbon-based spintronics has stimulated a number of recent theoretical studies on the RKKY interaction in graphene, with the aim of determining the most energetically favourable alignments between embedded magnetic moments. The RKKY interaction in undoped graphene decays faster than expected for conventional two-dimensional materials and recent studies suggest that the adsorption configurations favoured by many transition-metal impurities may lead to even shorter ranged decays and possible sign-changing oscillations. Here we show that these features emerge in a mathematically transparent manner when the symmetry of the configurations is included in the calculation. Furthermore, we show that by breaking the symmetry of the graphene lattice, via uniaxial strain, the decay rate, and hence the range, of the RKKY interaction can be significantly altered. Our results suggest that magnetic interactions between adsorbed impurities in graphene can be manipulated by careful strain engineering of such systems., Comment: 12 pages, 6 figures, submitted

The ease with which the physical properties of graphene can be tuned suggests a wide range of possible applications. Recently, strain engineering of these properties has been of particular interest. Possible spintronic applications of magnetically doped graphene systems have motivated recent theoretical investigations of the so-called Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between localized moments in graphene. In this work a combination of analytic and numerical techniques are used to examine the effects of uniaxial strain on such an interaction. A range of interesting features are uncovered depending on the separation and strain directions. Amplification, suppression, and oscillatory behavior are reported as a function of the strain and mathematically transparent expressions predicting these features are derived. Since a wide range of effects, including overall moment formation and magnetotransport response, are underpinned by such interactions we predict that the ability to manipulate the coupling by applying strain may lead to interesting spintronic applications., Comment: 6 pages, 3 figures

The growing interest in carbon-based spintronics has stimulated a number of recent theoretical studies on the RKKY interaction in graphene, based on which the energetically favourable alignment between magnetic moments embedded in this material can be calculated. The general consensus is that the strength of the RKKY interaction in graphene decays as 1/D3 or faster, where D is the separation between magnetic moments. Such an unusually fast decay for a 2-dimensional system suggests that the RKKY interaction may be too short ranged to be experimentally observed in graphene. Here we show in a mathematically transparent form that a far more long ranged interaction arises when the magnetic moments are taken out of their equilibrium positions and set in motion. We not only show that this dynamic version of the RKKY interaction in graphene decays far more slowly but also propose how it can be observed with currently available experimental methods., Comment: 7 pages, 2 figures, submitted

The magnetic properties of graphene-related materials and in particular the spin-polarised edge states predicted for pristine graphene nanoribbons (GNRs) with certain edge geometries have received much attention recently due to a range of possible technological applications. However, the magnetic properties of pristine GNRs are not predicted to be particularly robust in the presence of edge disorder. In this work, we examine the magnetic properties of GNRs doped with transition-metal atoms using a combination of mean-field Hubbard and Density Functional Theory techniques. The effect of impurity location on the magnetic moment of such dopants in GNRs is investigated for the two principal GNR edge geometries - armchair and zigzag. Moment profiles are calculated across the width of the ribbon for both substitutional and adsorbed impurities and regular features are observed for zigzag-edged GNRs in particular. Unlike the case of edge-state induced magnetisation, the moments of magnetic impurities embedded in GNRs are found to be particularly stable in the presence of edge disorder. Our results suggest that the magnetic properties of transition-metal doped GNRs are far more robust than those with moments arising intrinsically due to edge geometry., Comment: submitted

Among the many interesting features displayed by graphene, one of the most attractive is the simplicity with which its electronic structure can be described. The study of its physical properties is significantly simplified by the linear dispersion relation of electrons in a narrow range around the Fermi level. Unfortunately, the mathematical simplicity of graphene electrons is only limited to this narrow energy region and is useless when dealing with problems that involve energies outside the linear dispersion part of the spectrum. In this letter we remedy this limitation by deriving a set of closed-form analytical expressions for the real-space single-electron Green function of graphene which are valid across an enormous fraction of the energy spectrum. By extending to a wider energy range the simplicity with which graphene electrons are described, it is now possible to derive more mathematically transparent and insightful expressions for a number of physical properties that involve higher energy scales. The power of this new formalism is illustrated in the case of the magnetic (RKKY) interaction in graphene.

The electronic properties of low-dimensional materials can be engineered by doping, but in the case of graphene nanoribbons (GNR) the proximity of two symmetry-breaking edges introduces an additional dependence on the location of an impurity across the width of the ribbon. This introduces energetically favorable locations for impurities, leading to a degree of spatial segregation in the impurity concentration. We develop a simple model to calculate the change in energy of a GNR system with an arbitrary impurity as that impurity is moved across the ribbon and validate its findings by comparison with ab initio calculations. Although our results agree with previous works predicting the dominance of edge disorder in GNR, we argue that the distribution of adsorbed impurities across a ribbon may be controllable by external factors, namely an applied electric field. We propose that this control over impurity segregation may allow manipulation and fine-tuning of the magnetic and transport properties of GNRs., Comment: 5 pages, 4 figures, submitted

Motivated by recent studies reporting the formation of localized magnetic moments in doped graphene, we investigate the energetic cost for spin polarizing isolated impurities embedded in this material. When a well-known criterion for the formation of local magnetic moments in metals is applied to graphene we are able to predict the existence of magnetic moments in cases that are in clear contrast to previously reported Density Functional Theory (DFT) results. When generalized to periodically repeated impurities, a geometry so commonly used in most DFT-calculations, this criterion shows that the energy balance involved in such calculations contains unavoidable contributions from the long-ranged pairwise magnetic interactions between all impurities. This proves the fundamental inadequacy of the DFT-assumption of independent unit cells in the case of magnetically doped low-dimensional graphene-based materials. We show that this can be circumvented if more than one impurity per unit cell is considered, in which case the DFT results agree perfectly well with the criterion-based predictions for the onset of localized magnetic moments in graphene. Furthermore, the existence of such a criterion determining whether or not a magnetic moment is likely to arise within graphene will be instrumental for predicting the ideal materials for future carbon-based spintronic applications., Comment: Submitted to PRL